Employing the disordered local moment formalism in combination with a first-principles tight-binding linear muffin-tin orbital method we find that in disordered fcc ${\mathrm{Fe}}_{70}{\mathrm{Pt}}_{30}$ alloy the effective magnetic interaction changes from ferromagnetic to antiferromagnetic as the lattice constant is reduced from its equilibrium value at ambient pressure. This result explains recent experiments on this alloy that have claimed an appearance of the new magnetic spin-glass phase under high pressure. The value of the volume where the change in the magnetic interaction occurs is just slightly higher than the critical volume at which ${\mathrm{Fe}}_{70}{\mathrm{Pt}}_{30}$ becomes nonmagnetic, suggesting that under applied pressure the system exhibits two types of magnetic critical points. A comparison of our results with earlier theoretical studies of the fcc Fe-Ni Invar alloys reveals a similarity between the high-pressure magnetic state of ${\mathrm{Fe}}_{70}{\mathrm{Pt}}_{30}$ and the magnetic ground state of the Fe-Ni alloys at ambient pressure.
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